Where would I find the source files that pertain to the package listing in the software centre? I'm guessing the SC is just a window through which these listings are viewed, rather than being a part of the SC itself, so are these customised files found only in the Ubuntu variant of the package, or is it part of the upstream project?

As DoR says, the descriptions are stored inside the package. In a source package, they can be found in the debian/control file. As the description is part of the packaging, it isn't part of the upstream project. Though in most cases, we share the same description with Debian. We try to keep them in sync. Unless you're interested in getting more involved with Ubuntu development, simply file a bug against the package in question (you might also want to tag it "bite-sized" so new contributers can find it). A bug triager or developer will then determine whether the description should be fixed directly in Ubuntu or first in Debian. Generally, if there is no other difference between the Ubuntu and Debian package we try to get the bug fixed in Debian first.

Here's what a debian/control file looks like:

Source: hello
Section: devel
Priority: optional
Maintainer: Ubuntu Developers <ubuntu-devel-discuss@lists.ubuntu.com>
XSBC-Original-Maintainer: Santiago Vila <sanvila@debian.org>
Standards-Version: 3.9.1
Homepage: http://www.gnu.org/software/hello/
Package: hello
Architecture: any
Depends: ${shlibs:Depends}, dpkg (>= 1.15.4) | install-info
Description: The classic greeting, and a good example
The GNU hello program produces a familiar, friendly greeting. It
allows non-programmers to use a classic computer science tool which
would otherwise be unavailable to them.
.
Seriously, though: this is an example of how to do a Debian package.
It is the Debian version of the GNU Project's `hello world' program
(which is itself an example for the GNU Project).

Fixing small bugs like these is way to get you feet wet in both Ubuntu development and how to work with Debian packages. Find one you'd like to fix and try following this tutorial on the Ubuntu wiki.

The description for every package is stored inside the package, Software Center doesn't have anything to do with it. If there is a bug in a description for a package, file it against that package, not Software Center.